PORTLAND, Ore. -- A professor in solid-state physics, who ordinarily studies subjects such as thin-film deposition on semiconductors, took some time off to study home run hitters who take steroids. The Tufts University (Medford, Mass.) professor's surprising finding was that the use of steroids that add just 10 percent to muscle mass would increase bat speed by only 5 percent, enough to raise a slugger's home run production by a surprising 50 percent.

"I wanted to know why steroid use seems to affect home run hitters disproportionately," said physicist Roger Tobin. "What I found is that statistically, it only takes a small change in bat speed to result in a dramatic change in the number of home runs hit."

Babe Ruth's record of 60 home runs in a season held for 34 years until Roger Maris edged Ruth out by a single home run in 1961. That record held for 35 more years, until what Tobin calls the "dawn of the steroid era in sports," which he says was in the 1990s. During that time six players hit more than 60 home runs in a season, including Barry Bonds, who hit 73 home runs in 2001. This increase in the number of home runs, however, dropped back to normal levels after 2003, when major league baseball instituted steroid testing.

"Of course, this does not prove that Barry Bonds was taking steroids," said Tobin. "But it does mean that if he was taking them, then he may have hit 50 percent more home runs that he would without them, or about 50 in 2001 instead of 73."

The technical explanation is that home runs are at the "tail" of a normal, bell-shaped distribution of how far balls are hit, and statistically the tails are disproportionately affected by small changes in the distribution. In layman's terms, for long balls that land near the fence, it takes only a few more feet to turn them into home runs.

Tobin also studied pitchers' records to see if they too were disproportionately affected by steroid use. He found that an increase in muscle mass of 10 percent from the use of steroids would translate to an additional 5 percent in the speed of a pitcher's throws, taking a 90 mph fast ball up to just over 94 mph. However, that extra speed would reduce the pitcher's earned-run average by only about 0.5 per game, a much less dramatic improvement than for home run hitters.

Tobin's study will be published next month in the American Journal of Physics.